I have experienced the displacement of native fish on a smaller scale than the Great Lakes, many years ago. In fact, this ecological manipulation was one of the reasons I chose to attend school in pursuit of a degree in Marine Science.
Being in the aquarium industry as a profession, I may be more in touch with the issue of invasive exotic species than most people as a result. For instance, the incidental and designed release of cichlids such as tilapia, an aquarium fish from South America, into Florida waters many years ago displaced a great number of indigenous species, many of which could easily be considered game fish. The aquarium industry has been blamed to large extent or releasing these exotic species into the waters of the US; most recently, there was a huge issue in Maryland when some locals caught a snakehead (considered an ornamental aquarium fish), which is a fish originating in Southeastern Asia (kind of a cross between a largemouth and a pike), in a farm pond. The media and wildlife service freaked out, worried that these fish would invade other lakes and ponds and would quickly outcompete resident species such as largemouth for available resources... they're probably right, a snakehead is one tough sucker with the appetite of half a dozen largemouth of the same size. Still, whether released into the wild by accident or design, the issue now is how to keep it from happening again, and how to remedy the problem.
My own case was the lake I grew up on: at one time, it was full of nothing but hefty chain pickerel and bluegills. Then a "well-meaning" resident on the lake started dropping largemouth bass and bullhead catfish that he had caught in a nearby lake into our lake. Within three years, I went from catching nothing but pickerel to one pickerel every ten or twelve fish; pathetic. I'll take a pickerel, which actively stalks prey, over a bass, which sits around waiting for prey to swim by most of the time, anyday.
Biologists, wildlife officials, and miscellaneous people 50 years ago tried introducing foreign species into water systems plagued with some nuisance organism such as vegetation, crustaceans, mollusks, etc. The organisms flourished because they had the proper conditions in which to thrive, no natural predators present, and hence no population checks so long as the food kept coming. These people didn't understand that what they were doing would totally upset the balance of that ecosystem. Now, 50 years later, we're all trying to help clean up the mess left to us.
How do you control the problem? Culling. Cull the invasive species out of the systems. This includes, for example, rainbows and browns that have been moved to habitats that were otherwise populated by nothing more than brookies and cutt-throats, so far as displaced species are concerned. Re-introduce the original species if they are in need. Monitor populations. Quit trying to take care of a problem by creating another one; I'm quite certain that Mother Nature and evolution had things where they needed to be before we started messing around with them.